What Is Refraction
When a beam of light meets the boundary of another transparent medium, part of it is reflected back into the first medium and the rest enters the second. The ray that crosses the interface obliquely — that is, with an angle of incidence between 0° and 90° — changes its direction of propagation at the boundary. This change of direction is called refraction of light. A ray represents the direction of a narrow beam, and the angles of incidence and refraction are always measured from the normal to the interface, not from the surface itself.
The cause of the bending is a change in the speed of light between the two media. In an optically denser medium light travels more slowly, and the ray bends towards the normal; in an optically rarer medium it travels faster, and the ray bends away from the normal. The interface between the two media is where this adjustment happens.
A ray passing from a rarer to a denser medium bends towards the normal, so the angle of refraction $r$ is smaller than the angle of incidence $i$. (Based on NCERT Fig. 9.8 and NIOS Fig. 20.6.)
Snell's Law and Refractive Index
Experiments by Willebrord Snell led to the two laws of refraction. First, the incident ray, the refracted ray, and the normal to the interface at the point of incidence all lie in the same plane. Second, the ratio of the sine of the angle of incidence to the sine of the angle of refraction is a constant for a given pair of media. This second statement is Snell's law:
$$\frac{\sin i}{\sin r} = n_{21}$$
Here $n_{21}$ is the refractive index of the second medium with respect to the first. It is a characteristic of the pair of media and of the wavelength of the light, but it does not depend on the angle of incidence. In the symmetric form used widely in NEET problems, Snell's law reads $n_1 \sin i = n_2 \sin r$, where $n_1$ and $n_2$ are the (absolute) refractive indices of the two media.
If $n_{21} > 1$ then $r < i$ and the refracted ray bends towards the normal — medium 2 is optically denser. If $n_{21} < 1$ then $r > i$ and the ray bends away from the normal, which is the case for light passing from a denser medium into a rarer one.
Which medium's index sits on which side
In $n_1 \sin i = n_2 \sin r$, the index $n_1$ multiplies $\sin i$ on the incidence side and $n_2$ multiplies $\sin r$ on the refraction side. Students often invert this and write $n_1 \sin r = n_2 \sin i$, which reverses the predicted bending. Also note that optical density (set by the speed of light) is not the same as mass density: turpentine is optically denser than water yet has a smaller mass density.
Rule: pair each refractive index with the angle measured in that same medium. Bigger index ⇒ ray closer to the normal.
Refractive Index and Speed of Light
The refractive index of a medium also expresses how much light slows down inside it. The (absolute) refractive index equals the speed of light in vacuum divided by the speed of light in the medium:
$$n = \frac{c}{v}$$
Because $c$ is the maximum possible speed, $n \ge 1$ for any material medium, and a larger $n$ means a slower wave. The refractive index of medium 2 with respect to medium 1 can equivalently be written as the ratio of the speed in medium 1 to the speed in medium 2, $n_{21} = v_1/v_2$, which is the form NIOS uses. The table below lists standard values referenced to air or vacuum.
| Medium | Refractive index n | Note |
|---|---|---|
| Vacuum / air | 1.00 | Reference medium |
| Water | 1.33 | Denser than air, rarer than glass |
| Ordinary glass | 1.50 | — |
| Crown glass | 1.52 | Denser than ordinary glass |
| Dense flint glass | 1.62 – 1.65 | NCERT 1.62; NIOS 1.65 |
| Diamond | 2.42 | Highest among common solids |
Frequency stays fixed; speed and wavelength change
On refraction, the frequency of the light is set by the source and does not change. What changes is the speed $v$ and therefore the wavelength $\lambda$. Since $n = c/v$, in a denser medium the speed drops and the wavelength shrinks by the same factor ($\lambda_{\text{medium}} = \lambda_{\text{vacuum}}/n$). Colour is tied to frequency, so the colour of monochromatic light does not change inside glass or water.
Rule: $f$ unchanged, $v$ and $\lambda$ both decrease by a factor of $n$ on entering a denser medium.
Relative Index and Reversibility
Refractive indices for any pair of media combine through simple rules. If $n_{21}$ is the index of medium 2 with respect to medium 1 and $n_{12}$ that of medium 1 with respect to medium 2, then the principle of reversibility of light requires that the reversed ray retrace its path. This gives:
$$n_{12} = \frac{1}{n_{21}}$$
For three media there is a chaining rule: $n_{32} = n_{31} \times n_{12}$, where each subscript pair denotes one index. A common application is finding the index of glass with respect to water from their air values, $n_{wg} = n_{ag}/n_{aw}$ — for $n_{ag} = 1.52$ and $n_{aw} = 1.33$ this gives $1.14$.
When a ray in a denser medium hits the boundary beyond the critical angle, refraction fails entirely. See Total Internal Reflection for how Snell's law sets that limit.
Apparent Depth and Normal Shift
A familiar consequence of refraction is that the bottom of a water tank appears raised. Rays leaving an object at the bottom bend away from the normal as they pass from water into air, so to an observer looking from above they seem to diverge from a point nearer the surface. For viewing close to the normal direction, the apparent depth equals the real depth divided by the refractive index of the medium:
$$\text{apparent depth} = \frac{\text{real depth}}{n}$$
The difference between real and apparent depth is the normal shift, $\Delta = \text{real depth} - \text{apparent depth} = h\left(1 - \tfrac{1}{n}\right)$. Because $n > 1$, the apparent depth is always less than the real depth, which is why a swimming pool looks shallower than it is.
The emergent ray (teal) bends away from the normal; projected back, it places the image at depth $h/n$, shallower than the real depth $h$. (Based on NCERT Fig. 9.10.)
Lateral Shift Through a Slab
For a rectangular glass slab, refraction occurs at two parallel interfaces: air-to-glass on entry and glass-to-air on exit. Applying Snell's law at both faces shows that the angle at which the ray emerges equals the original angle of incidence, so the emergent ray is parallel to the incident ray. There is no net deviation in direction, but the ray is displaced sideways. This sideways displacement is the lateral shift.
The lateral shift grows with the thickness of the slab and with the angle of incidence, and vanishes at normal incidence. It is the reason an object viewed through a thick glass block appears slightly offset from its true position.
Across two parallel faces the deviations cancel, so the emergent ray is parallel to the incident ray but offset by the lateral shift $d$. (Based on NCERT Fig. 9.9.)
Worked Examples
Calculate the speed of light in water if its refractive index with respect to air is $4/3$. Take the speed of light in vacuum as $c = 3 \times 10^{8}\ \text{m s}^{-1}$.
Using $n = c/v$, the speed in water is $v = c/n = (3 \times 10^{8})/(4/3) = 2.25 \times 10^{8}\ \text{m s}^{-1}$. Light slows to about three-quarters of its vacuum speed inside water.
A ray of light is incident at 30° at a water–glass interface. Find the angle of refraction in glass, given $n_{ag} = 1.5$ and $n_{aw} = 1.3$.
For the water–glass interface, $\dfrac{\sin i_w}{\sin i_g} = \dfrac{n_{ag}}{n_{aw}} = \dfrac{1.5}{1.3}$. Then $\sin i_g = \dfrac{1.3}{1.5}\sin 30^\circ = 0.4446$, so the angle of refraction in glass is about $25^\circ 41'$.
A tank is filled with water to a height of 12.5 cm. The apparent depth of a needle at the bottom, measured by a microscope, is 9.4 cm. Find the refractive index of water.
Using $\text{apparent depth} = \dfrac{\text{real depth}}{n}$, we get $n = \dfrac{\text{real depth}}{\text{apparent depth}} = \dfrac{12.5}{9.4} \approx 1.33$, the standard value for water.
Refraction in one screen
- Refraction is the bending of light at the boundary of two media, caused by a change in speed.
- Snell's law: $n_1 \sin i = n_2 \sin r$; the index is independent of the angle of incidence but depends on wavelength.
- Refractive index $n = c/v \ge 1$; denser medium ⇒ smaller speed, ray bends towards the normal.
- Reversibility gives $n_{12} = 1/n_{21}$; chaining gives $n_{32} = n_{31} \times n_{12}$.
- Apparent depth $= $ real depth$/n$; the normal shift is $h(1 - 1/n)$.
- A parallel slab causes lateral shift but no net deviation; frequency is unchanged while speed and wavelength shrink.